Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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<
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.</
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<
s
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xml:space
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cere quæ Cycloidem tangat.</
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</
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<
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<
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xml:space
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">Sit cyclois A B C, & </
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xml:space
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">punctum in ea datum B, per quod
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<
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xlink:href
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xml:space
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Fig. 2.</
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tangentem ducere oporteat.</
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</
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<
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<
s
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echoid-s1482
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xml:space
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">Circa axem cycloidis A D deſcribatur circulus genitor
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A E D, & </
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<
s
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echoid-s1483
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xml:space
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">ducatur B E parallela baſi cycloidis, quæ dicto
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circulo occurrat in E, & </
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<
s
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echoid-s1484
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xml:space
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">jungatur A E, cui denique paral-
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lela per B agatur H B N. </
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<
s
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echoid-s1485
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xml:space
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">Dico hanc cycloidem in B con-
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tingere.</
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<
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</
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<
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<
s
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xml:space
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">Sumatur enim in ea punctum quodlibet, à B diverſum,
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ac primo verſus ſuperiora velut H, & </
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<
s
xml:id
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xml:space
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">per H ducantur re-
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cta baſi cycloidis parallela, quæ occurrat cycloidi in L, cir-
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culo A E D in K, rectæ A E in M. </
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<
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xml:space
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">Quia ergo K L eſt
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æqualis arcui K A, recta autem K M minor arcu K E, erit
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recta M L minor arcu A E, hoc eſt, rectâ E B, ſive M H;
<
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</
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<
s
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xml:space
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">unde apparet punctum H eſſe extra cycloidem.</
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<
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</
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<
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<
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xml:space
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">Deinde in recta H N ſumatur punctum N inferius B, & </
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<
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per N agatur, ut ante, baſi parallela, quæ occurrat cycloi-
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di in Q, circulo A E D in O, rectæ A E productæ in P.
<
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</
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<
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xml:space
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">Quia ergo O Q, æqualis eſt arcui O A; </
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<
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xml:space
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">O P autem major
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arcu O E; </
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<
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xml:space
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">erit P Q minor arcu E A, hoc eſt, rectâ E B,
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ſive P N. </
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<
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xml:space
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">Unde apparet rurſus punctum N eſſe extra cycloi-
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dem. </
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<
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xml:space
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">Cum igitur quodlibet punctum præter B, in recta
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H B N ſumptum, ſit extra cycloidem, conſtat illam in
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puncto B cycloidem contingere; </
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<
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">quod erat demonſtrandum.</
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<
s
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xml:space
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">Huic demonſtrationi an locum ſuum hic relinquerem dubi-
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tavi, quod non multum ei abſimilem à clariſſimo Wrennio
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editam inveniam in libro Walliſii de Cycloide. </
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<
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xml:space
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& </
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<
s
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">univerſali conſtructione propoſitum abſolvi, quæ non cy-
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cloidi tantum ſed & </
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<
s
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">aliis curvis, ex cujuſlibet figuræ circum-
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volutione genitis, conveniat; </
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<
s
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">dummodo ſit figura in ean-
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dem partem cava, & </
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<
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<
s
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">Sit enim curva N A B, orta ex circumvolutione figuræ
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<
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Fig. 3.</
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